SQL & PL/SQL :: Finding Number Of Pattern Occurrences In String?

The code which I am working on consists of an incoming dynamic string which be in the form of binary digits. The max size of the string will be 12 digits. For example, the string can be '111011000001', '000000000000', '111111011111', etc.

I need to find the number of occurences of '111' in the incoming string. Say in the 1st example, result will be 1, in the 2nd example result will be 0, and in the third example, the result will be 3.

I have been trying to capture the string length and replacing the variables '111' to find the number of occurences, but it isn't giving me the result that I want. This is what I have tried

SQL> conn hr/hr
Connected.
SQL> show user
USER is "HR"

[Code]....

I searched the forum and found a similar topic, and following that guideline, I even tried dividing the string with the length of the pattern. It works in some scenarios (the first and second examples mentioned below), while it fails in some scenarios (third example mentioned below)

SQL> select (length('11101110111') - length(replace('11101110111','111','')))/length('111') as occurences from dual;

OCCURENCES
----------
3

SQL> select (length('110111110111') - length(replace('110111110111','111','')))/length('111') as occurences from dual;

OCCURENCES
----------
2

SQL> select (length('111111111111') - length(replace('111111111111','111','')))/length('111') as occurences from dual;

OCCURENCES
----------

SQL>